Imaging phenotypes. Gliomas contain various heterogeneous subregions broadly categorized into three groups: necrosis and non-enhancing core, edema, and enhancing core. These subregions reflect differences in tumor biology, have variable histologic and genomic phenotypes, and exhibit highly variable clinical prognosis [1]}. Typically, the area of dead cells in the center is referred to as necrosis or non-enhancing core, and the tissue swelling caused in the outer region due to accumulation of fluid is referred to as edema (mayfieldclinic.com/pe-braintumor.htm). Following suit, we divide the tumor region for each subject into \(\tau =3\)  spherical shells, i.e., one inner sphere and two spherical shells. For each subject, we follow the procedure described in Algorithm S1 to construct the PDFs corresponding to the three spherical shells. The PDFs estimated in each layer are used to construct the PC scores \(Y^{(t)}\) , which act as the imaging phenotypes.
